Mapping intrinsic electromechanical responses at the nanoscale via sequential excitation scanning probe microscopy empowered by deep data

Abstract

Ever-increasing hardware capabilities and computation powers have enabled acquisition and analysis of big scientific data at the nanoscale routine, though much of the data acquired often turn out to be redundant, noisy and/or irrelevant to the problems of interest, and it remains nontrivial to draw clear mechanistic insights from pure data analytics. In this work, we use scanning probe microscopy (SPM) as an example to demonstrate deep data methodology for nanosciences, transitioning from brute-force analytics such as data mining, correlation analysis and unsupervised classification to informed and/or targeted causative data analytics built on sound physical understanding. Three key ingredients of such deep data analytics are presented. A sequential excitation scanning probe microscopy (SE-SPM) technique is first developed to acquire high-quality, efficient and physically relevant data, which can be easily implemented on any standard atomic force microscope (AFM). Brute-force physical analysis is then carried out using a simple harmonic oscillator (SHO) model, enabling us to derive intrinsic electromechanical coupling of interest. Finally, principal component analysis (PCA) is carried out, which not only speeds up the analysis by four orders of magnitude, but also allows a clear physical interpretation of its modes in combination with SHO analysis. A rough piezoelectric material has been probed using such a strategy, enabling us to map its intrinsic electromechanical properties at the nanoscale with high fidelity, where conventional methods fail. The SE in combination with deep data methodology can be easily adapted for other SPM techniques to probe a wide range of functional phenomena at the nanoscale.

Keywords: principal component analysis; scanning probe microscopy; sequential excitation; simple harmonic oscillator model.

Figure 1.

The schematics of dynamic SPM experiments based on DART, BE and SE techniques, wherein the AC waveforms combining two distinct or a band of frequencies are synthesized to excite the sample under DART or BE, respectively, while a sequence of AC waveforms with different frequencies are used to excite the sample under SE.

Figure 2.

A sequence of SE-PFM amplitude mappings obtained at distinct frequen-cies in PZT ceramic.

Figure 3.

Comparison of PZT mappings acquired by SE-PFM and DART-PFM processed via SHO; (a) SHO fitting of SE-PFM spectrum data for one representative pixel; (b) rough topography mapping; and (c)–(e) reconstructed SE-PFM mappings of (c) intrinsic amplitude , (d) resonance frequency and (e) quality factor ; (f)–(h) reconstructed DART-PFM mappings of (f) the intrinsic amplitude, (g) resonance frequency and (h) quality factor obtained, wherein white areas show points where SHO analysis fails.

Figure 4.

Comparison of PCA and SHO expansion for SE-PFM data of PZT; (a) first three PCA spectral eigenvectors in comparison with corresponding SHO spectral basis; (b) first three PCA spatial eigenvectors; (c) corresponding SHO spatial basis.

Figure 5.

Comparison of PCA and SHO expansion for a three-phase model system with distributions of intrinsic amplitude, resonant frequency and quality factor specified in (a), from which the SE-PFM mappings can be constructed based on SHO; (b) comparison of first three spectral eigenvectors of PCA and corresponding SHO spectral basis; (c) the first three spatial eigenvectors of PCA; (d) corresponding SHO spatial basis.